How can i copy the object position to the edit position to meet the rest position?
Any movement done in pose mode will also be shown in object mode, any keyframed movement will change this position as you change the current frame.

One option you have is to clear any pose mode changes made. While in pose mode press &#9095; AltG, &#9095; AltR and &#9095; AltS to clear the location, rotation and scale of the selected bones, putting the armature back into the rest position.

Another option is to set the current position as the rest position by pressing &#9096; CtrlA and choosing "Apply pose as Rest Pose"